Resolução -Hazzan-cap_2

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1
Hazzan & Pompeo Capítulo 2 
Juros Simples 
 
 
Exercício 1 
 
a) 
00,1205012,000,000.2 =××=
⋅⋅=
j
niCj
 
 
b) 00,260.1221,000,000.3 =××=j 
 
c) 00,93636013,000,000.2 =××=j 
 
d) 00,000.91015,000,00.6 =××=j 
 
 
Exercício 2 
 
33,333.21
12
580,000,000.1600,000.16 =→××+=+= MjcM 
 
 
Exercício 3 
 
00,070.1
12
242,000,000.100,000.1 =→××+= MM 
 
 
Exercício 4 
 
..%505,0
00,000.180
00,000.9
600,000.3000,000.3000,000.39
mai
i
jCM
→==
××+=
+=
 
 
 
 
 
 
 
 
 
 2
Exercício 5 
 
anosn
n
jCM
66
00,300
00,800.1
10,000,000.300,000.300,800.4
→==
××+=
+=
 
 
 
Exercício 6 
 
00,36000,000.500,360.500,000.5
072.1
00,360.5
)072,01(00,360.5
4018,000,360.5
=→−=−=⇒==
+×=
××+=
+=
jCMjC
C
CC
jCM
 
 
 
 
Exercício 7 
 
anosn
n
niCCM
jCM
44
96
384
12,000,80000,80000,184.1
00,184.100,38400,800
→==
××+=
⋅⋅+=
=+=+=
 
 
 
Exercício 8 
 
..%57,30357,0
00,200.4
00,150
400,050.100,050.100,200.1
mai
i
→==
××+=
 
 
 
Exercício 9 
 
..%99,50599,0
2)2,000,400.200,400.2()2,000,400.200,400.2(00,150.2
mai
i
→=
×××−+×−=
 
 
 
 
 3
Exercício 10 
 
.125,12
08,0
1
)08,01(2
08,02
meioeanosn
nCC
nCCC
jCM
→==
×+×=⋅
××+=⋅
+=
 
 
Exercício 11 
 
mesesn
nCC
nCCC
jCM
2525
08,0
2
)08,01(3
08,03
→==
×+×=⋅
××+=⋅
==
 
 
 
Exercício 12 
 
mesesn
niCiC
niCCM
iCCM
44
416
44
16
1111
1112
1111
→=
××⋅=××
××⋅+⋅=
××+=
 
 
 
Exercício 13 
 
mesesn
n
nn
nn
MM
nM
nM
4333,0
00,857.2260,571.68
40,428.26700,857.2200,000.336
20,100,857.22268,100,000.20000,000.200
20,100,857.22200,857.222
68,100,000.20000,000.200
21
2
1
≅→=
=⋅
⋅+=⋅
××=××+
=
××+=
××+=
 
 
 
 
 
 
 4
Exercício 14 
 
→+= jCM
00,500
00,100.1
2
1
=
=
C
C
 
..%12
300,100.100,,396
00,39600,15000,246310,000,50000,246
00,100.1
1
1
112
11
111
222
mai
i
jj
nij
niCj
niCj
=
××=
=+=××=−=
××=
××=
××=
 
 
Exercício 15 
 
..%3030,0
08,007,015,0
32,025,0
28,025,0
30,05,01
1
25,0
25,0
5,0
321
3
2
111
3
2
1
321
aaii
CCCiC
jjjj
Cj
Cj
CiCj
iCj
CC
CC
CC
CCCC
=→=
⋅+⋅+⋅=×
××=
×⋅=
×⋅=
×⋅=××=
××=
⋅=
⋅=
⋅=
++=
 
 
 
Exercício 16 
 
 1.000,00 sacas de café× 00,000.3$
saca
R 
 
 R$ 3.000.000,00 
 
mesesn
mai
3
..%5
=
= 
 
venda final=R$ 2.400.000,00 
 5
00,000.450.3
305,000,000.000.300,000.000.3
=
××+=
M
M
 
 
00,000.050.1$
00,000.400.2
R
− 
 
R$1.050.000,00 → prejuízo real 
 
 
Exercício 17 
 
30.000,00 sacas→ 00,5$
saca
R 
 
 R$ 150.000,00 
 
 
6 meses depois 00,12$
saca
Rvende⎯⎯ →⎯ 
 
30.000 sacas 00,12$
saca
R
× 
 
 R$ 360,00 
 
..%12 aai = (juros simples) 
)(00,000.102$
00,000.360$
00,000.258$
612,000,000.15000,000.150
12
2
1
1
lucroRMM
RM
RM
jCM
=−
=
=
××+=+=
 
 
 
Exercício 18 
 
00,000.250$
5,4)7,28,1(00,000.125.1
1510,08,18,100,000.125.1
00,000.125.11510,0
8,1)8,01(
1008,0
1
11
11
112
111
211
RC
CC
CC
MMM
CCM
CCM
=
⋅=+⋅=
××⋅+⋅=
=××+=
⋅=+⋅=
××+=
 
 
 
 6
Exercício 19 
 
80,172$8,000,216
00,216.4
3018,000,000.400,000.4
3018,0
1
1
111
Rj
M
M
CCM
=×=
=
××+=
××+=
 
 
a) 80,172.4=liqM 
 
b) 
92,450.3$
)0432,01(00,600.3
80,03018,000,600.3
1
1
11
RC
C
CCM liq
=
+⋅=
×××+==
 
 
Exercício 20 
 
a) 
00,704.12
0587,000,000.1200,000.12
80,04
12
22,0
2
2
111
=
×+=
×××+=
liq
liq
liq
M
M
CCM
 
 
b) 
38,862.10$
)0587,01(00,500.11
80,04
12
22,000,500.11
1
1
11
RC
C
CC
=
+⋅=
×××+=
 
 
Exercício 21 
 
00,200.121 =+= CCC 
 
310,0
208,0
22
11
×⋅+=
×⋅+=
CCM
CCM
212121 12068,13,116,1)30,01()16,01( CCCCCC ⋅=→⋅=⋅→+⋅=+⋅∴ 
 
15,63485,565$
00,2000.112068.1
00,200.1
12
22
21
=→−
=+⋅
=+
CRC
CC
CC
 
 
 Errado 
 7
 
61,78239,471
00,200.1875,1
00,200.1
875,1
30,016,0
310,0208,0
12
22
21
21
21
21
21
=→=
=+⋅
=+
⋅=
⋅=⋅
×⋅=×⋅
=
CC
CC
CC
CC
CC
CC
jj
 
 
 
Exercício 22 
 
00,800.100,200.1
00,38432,0
00,824.18,048,000,440.1
00,824.18,0)00,000.3(48,0
:log
00,000.3:
00,824.180,048,0
00,824.1810,0608,0
00,824.1
81,0
608,0
00,000.3
12
2
22
22
21
21
21
21
222
111
21
=∴=
=⋅
=⋅+⋅−
=⋅+−⋅
−=
=⋅+⋅
=×⋅+×⋅
=+
×⋅+=
×⋅+=
=+
CC
C
CC
CC
o
CCmas
CC
CC
jj
CCM
CCM
CC
 
 
 
Exercício 23 
 
a) 
..%18125,1
..%5,1
aa
ma
=×
 
 
b) 
..%1565,2
..%5,2
aa
ba
=×
 
 
c) 
..%1445,3
..%5,3
aa
ta
=×
 
 
 8
d) 
..%5,1335,4
..%5,4
aa
qa
=×
 
 
e) 
..%1325,6
..%5,6
aa
sa
=×
 
 
 
Exercício 24 
 
..%6,63%2,2
..%2,2..%4,4
ta
maba
=×
=
 
 
 
Exercício 25 
 
R$4.000,00 
 
Taxa=3,5%a.a. ; n=7meses 
 
%416,207..%2916,
12
35
=×= ma em 7 meses 
$20416,000,000.4$ RR =× 816,64 (juros simples em 7 meses) 
 
 
Exercício 26 
 
00,000.6
5
12
48,000,000.500,000.5
=
××+=
⋅⋅+=
M
M
niCCM
 
 
 
Exercício 27 
 
71,376.167
365
30,000,000.251 =××=j (juros exatos) 
83,395.167
360
30,000,000.252 =××=j (juros comerciais) 
 
 
 9
 
Exercício 28 
 
33,243
360
600.87
360
600.87
365
00,240
==
××=
=⋅⋅→××=
⋅⋅=
j
niCj
niCniC
niCj
 
 
 
Exercício 30 
 
a) 00,600.56
12
24,000,000.500,000.5 =→××+=→⋅⋅+= MMniCCM 
 
 
b) nniCj ⋅×=→⋅⋅= 24,000,000.500,000.5 
 
meses
anomess
anosn
50
/12
167,4
×
=
 
 
 
Exercício 32 
 
00,352.4544
360
96,000,000.3
38,292.4544
365
96,000,000.3
=→××=
=→××=
CC
EE
jj
jj
 
 
 
Exercício 33 
 
..%9090,04
12
00,000.000.2)00,000.000.200,000.6000.2( aaii
niCj
→=→××=−
⋅⋅=
 
 
 
 
 
 
 10
Exercício 34 
 
niCj ⋅⋅=1 
47
360
00,800
83
360
00,680
2
1
××=
××=
ij
ij
 
..%180
20,94
33,52
77,15620,9444,104
44,10483
360
00,68020,94
20,94
22
21
aaii
ii
ijij
jj
=→=
⋅=+⋅
⋅=→××=+
∴+=
 
 
 
Exercício 35 
 
00,000.350
29166,096,01
00,000.448
..%969599,0
29298,028125,0
66666,0137368,028125,1
66666,01)29166,01(
00,000.447
00,000.574
)66666,01(
)29166,01(
00,000.44800,000.574
0,8
12
00,000.574
)29166,01(
00,000.4485,3
12
00,000.448
=
×+
=
=→=
×=
×+=×+
×+=×+×
×+×
×+
=
××+=
×+
=→××+=
⋅⋅+=
C
aaii
i
ii
ii
i
i
iCC
i
CiCC
niCCM
 
 
 
 
 
 
 
 
 11
Exercício 36 
 
00,200.100,800
00,20025,0
00,520275,025,000,500
00,520275,0)00,000.2(25,0
00,000.200,000.2
,
00,520275,025,000,520
275,045
360
20,2
25,045
360
00,2
00,000.2
12
2
22
22
2121
2121
222
111
21
=∴=
=⋅
=⋅+⋅−
=⋅+−×
−=→=+
=⋅+⋅→=+
⋅=××=
⋅=××=
=+
CC
C
CC
CC
CCCC
mas
CCjj
CCj
CCj
CC
 
 
 
Exercício 37 
 
a) 1
30
05,0000.000.4000.000.41 ××+=M 
 
23,360.021.4
1
30
056,066,867.013.400,867.013.4
66,867.013.4
1
30
54,066,666.006.466,666.006.4
00,666.006.4
3
3
2
2
1
=
××+=
=
××+=
=
M
M
M
M
M
 
 
b) %530053,0
00,000.000.4
00,000.000.423,360.021.4
→=
− (no período) 
 
 
Exercício 38 
 
a) 1
30
024,0000.000.4000.000.41 ××==M 
 12
 
85,405.008.4
1
30
019,080,868.005.480,868.005.4
80,868.005.4
1
30
02,0200.003.4200.003.4
00,200.003.4
3
3
2
2
1
=
××+=
=
××+=
=
M
M
M
M
M
 
 
b) %21,00021,0
00,000.000.4
00,000.000.485,405.008.4
→=
− (no período) 
 
 
Exercício 39 
 
)%(270027,1000966,1000866,1000866,1
..%0966,0
30
%9,2;..%0866,0
30
%6,2
períodono
dada
→=××
==
 
 
 
Exercício 40 
 
)%(37,0003737,1)000933,1(
..%0933,0
30
%8,2
4 períodono
da
→=
=
 
 
 
Exercício 41 
 
 50.000,00 
 8 meses 
 i=2% a.m. 
 
 
a) %16..%28 =× mameses 
 
44,103.43
16,1)16,01(00,000.50
8200,000.50
=
⋅=+⋅=
××+==
C
CC
CCM
 
 
b) 47.103,44C)06,01(302,000,000.50 =→+⋅=××+= CCC 
 
c) 83,642.44)12,01(602,000,000.50 =→+⋅=××+= CCCC 
 13
Exercício 42 
 24.000,00 
 10 meses 
 
a) 13,672.19)022,01(022,000,000.24 =→+⋅=×+= CCCC 
 
b) 45,263.22)078,01(3026,000,000.24 =→+⋅=××+= CCCC 
 
c) ..%07,0
30
%1,2 da= 
52,955.22)0455,01(650007,000,000.24 =→+⋅=××+= CCCC 
 
 
Exercício 43 
 
89,001.58)056,01(2028,000,250.61
00,250.61
9025,000,000.500,000.50
=→+⋅=××+=
=
××+=
CCCC
M
M
 
 
 
Exercício 44 
 
..%286,202286,0
716004,000,000.50
00,000.5089,001.58
%5,17%5,27
ma
meses
meses
→
÷=
−
=×
 
 
Exercício 45 
 
88,256.68
)09,01(4
12
27,000,400.74
00,400.749
12
32,000,000.6000,000.60
=
+⋅=××+=
=××+=
C
CCC
M
 
 
Exercício 46 
 
..%75,202752,0
51376,0
00,000.60
00,000.6088,256.68
ma
meses
→
÷=
−